Question

a system with no solution occurs when the lines are

intersecting
parallel
overlapping
perpendicular

Explanation:

Define a system of equations and its solutions

Using the System of Equations Definition knowledge point
A system of linear equations represents two or more lines. A solution to the system is any point where the lines intersect.

Classify systems based on line relationships

Using the Systems of Equations Classification knowledge point

• Intersecting lines cross at exactly one point, representing a system with one unique solution.
• Overlapping lines (coincident lines) lie directly on top of each other, representing infinitely many solutions.
• Parallel lines run in the same direction and never cross, representing a system with no solution.
• Perpendicular lines are a special case of intersecting lines that cross at a \(90^\circ\) angle, representing exactly one solution.

Determine the correct option

Since the question asks for the condition when a system has "no solution," the lines must never intersect. Therefore, the lines must be parallel.

Answer:

• intersecting
• parallel (Correct answer)
• overlapping
• perpendicular